How circulation relates to lift (with demo)

After continually hearing the half-explained answer to how lift is achieved over an airplane wing, we decided to tell the whole story. It is well known that lift occurs when the pressure on the bottom of the wind is greater than the pressure on the top, and this pressure difference over comes the weight of the aircraft and obtains lift. This pressure difference is often explained as a Bernoulli problem where the airfoil causes the velocity at the top to be faster than the velocity on the bottom and that is how you get the pressure difference. We wanted to answer WHY this velocity is greater at the top. it is NOT because an air parcel hits the front of the air foil and separates and has to reattach at the end, this has been shown to be wrong in experimental visualization. The velocity difference is a result of Kelvin's theorem (the circulation around a closed contour is conserved). Imagine a plane on a runway. Initially the plane is at rest and therefore the circulation around the wing is 0. When the plane starts to move it sheds a vortex called the startup vortex, which stays at the beginning of the runway. As the plane moves down the runway it needs to maintain zero net circulation and therefore a counter-rotating vortex is generated around the wing. This vortex accelerates the air above the wing and slows the air below the wing down. And THAT is why you get a velocity difference leading to a pressure difference and eventually lift. The demo in this video tries to show the startup vortex and counter-rotating vortex generated upstream.